12 papers
Warped product spaces: Gromov hyperbolicity and identification of the visual boundary
Josh Kline, Nageswari Shanmugalingam, Gareth Speight +1
In this paper, we consider warped product spaces , where is a complete geodesic Gromov hyperbolic space, is a compact geodesic metric space, and the warping fu…
On the equivalence of BV notions in metric measure spaces
Luigi Ambrosio, Enrico Pasqualetto, Nageswari Shanmugalingam
The aim of the paper is to compare in detail several notions of space of functions of bounded variation in metric measure spaces . Informall…
Approximation of harmonic functions on metric measure spaces of controlled geometry via discrete graphs
Almaz Butaev, Liangbing Luo, Nageswari Shanmugalingam
Given a complete doubling metric measure space that supports a -Poincaré inequality, we approximate harmonic functions on a bounded domain with a prescribed Newton-Sob…
Fractional -Laplacians via Neumann problems in unbounded metric measure spaces
Luca Capogna, Ryan Gibara, Riikka Korte +1
We prove well-posedness, Harnack inequality and sharp regularity of solutions to a fractional -Laplace non-homogeneous equation , with , , for…
Traces of Newton-Sobolev functions on the visible boundary of domains in doubling metric measure spaces supporting a -Poincaré inequality
Sylvester Eriksson-Bique, Ryan Gibara, Riikka Korte +1
We consider the question of whether a domain with uniformly thick boundary at all locations and at all scales has a large portion of its boundary visible from the interior; here, "…
Solving Dirichlet problem on unbounded uniform domains by using sphericalization techniques
Riikka Korte, Sari Rogovin, Nageswari Shanmugalingam +1
Within the setting of metric spaces equipped with a doubling measure and supporting a -Poincaré inequality, establishing existence of solutions to Dirichlet problem in a bounde…